Utkal University, Odisha, Mathematics Semester 3, Partial Differential Equations and System of ODEs Syllabus

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Unit - 1 Partial Differential Equations

Unit 1

Partial Differential Equations

1.1 Partial Differential Equations Basic concepts and Definitions Mathematical Problems

1.2 First Order Equations Classification Construction and Geometrical Interpretation

1.3 Method of Characteristics for obtaining General Solution of Quasi Linear Equations

1.4 Method of Separation of Variables for solving first order partial differential equations.

Unit - 2 Derivation Of Heat Equation, Wave Equation And Laplace Equation

Unit 2

Derivation of Heat equation

2.1 Derivation of Heat equation Wave equation and Laplace equation

2.2 Classification of second order linear equations as hyperbolic parabolic or elliptic

2.3 Reduction of second order Linear Equations to canonical forms

Unit - 3 The Cauchy Problem

Unit 3

The Cauchy problem

3.1 The Cauchy problem Cauchy problem of an infinite string

3.2 Initial Boundary Value Problems SemiInfinite String with a fixed end SemiInfinite String with a Free end

3.3 Equations with nonhomogeneous boundary conditions Non Homogeneous Wave Equation

3.4 Method of separation of variables

3.5 Solving the Vibrating String Problem Solving the Heat Conduction problem

Unit - 4 Systems Of Linear Differential Equations

Unit 4

Systems of linear differential equations

4.1 Systems of linear differential equations Types of linear systems

4.2 Differential operators an operator method for linear systems with constant coefficients

4.3 Basic Theory of linear systems in normal form

4.4 Homogeneous linear systems with constant coefficients Two Equations in two unknown functions

4.5 The method of successive approximations

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Other Subjects of Semester-3
Group theory-i
Theory of real functions
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